Bayesian Statistics: An Introduction, 4th Edition

6.7 The general linear model

6.7.1 Formulation of the general linear model

All of the last few sections have been concerned with particular cases of the so-called general linear model. It is possible to treat them all at once in an approach using matrix theory. In most of this book, substantial use of matrix theory has been avoided, but if the reader has some knowledge of matrices this section may be helpful, in that the intention here is to put some of the models already considered into the form of the general linear model. An understanding of how these models can be put into such a framework, will put the reader in a good position to approach the theory in its full generality, as it is dealt with in such works as Box and Tiao (1992).

It is important to distinguish row vectors from column vectors. We write for a column vector and for its transpose; similarly if is an matrix then is its transpose. Consider a situation in which we have a column vector of observations, so that (the ...